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Testing, Estimation and Higher Order Expansions in GMM with Semi-Weak Instruments


  • Mehmet Caner


In this paper we analyze GMM with semi-weak instruments. This case includes the standard GMM and the nearly-weak GMM. In the nearly-weak GMM the correlation between the instruments and the first order conditions decline at a slower rate than root T. We find an important difference between the semi-weak case and the weak case. Inference with point estimates are possible with Wald, Likelihood ratio and LM tests in GMM with semi-weak instruments. This is important from an applied perspective since tests on the weak case do depnd on the true value and can only test simple null. Even though we may have all nearly-weak instruments in GMM it is still possible to test various hypotheses of interest. We also find a difference between the two subcategories in the semi-weak case. We derive higher order expansions for test statistics in the semi-weak case, and we show that with declining quality of instrumnents finite sample behavior of these tests get worser, so standard GMM finite sample behavior is always better than nearly-weak GMM. Unlike standard GMM, in the nearly-weak GMM we cannot eliminate the second order terms from these test statistics expansions.

Suggested Citation

  • Mehmet Caner, 2004. "Testing, Estimation and Higher Order Expansions in GMM with Semi-Weak Instruments," Econometric Society 2004 North American Summer Meetings 128, Econometric Society.
  • Handle: RePEc:ecm:nasm04:128

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    Cited by:

    1. Iglesias, Emma M. & Phillips, Garry D.A., 2011. "Almost Unbiased Estimation in Simultaneous Equations Models with Strong and / or Weak Instruments," Cardiff Economics Working Papers E2011/19, Cardiff University, Cardiff Business School, Economics Section.

    More about this item


    nearly-weak instruments; Wald statistics; Empirical process;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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